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Resolución de integrales/ 2^x+1/ 3^-x(7+2^x+1)

Integral de 3^-x(7+2^x+1) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                    
  /                    
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 |   -x /     x    \   
 |  3  *\7 + 2  + 1/ dx
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/                      
0
∫013−x((2x+7)+1) dx\int\limits_{0}^{1} 3^{- x} \left(\left(2^{x} + 7\right) + 1\right)\, dx 
Integral(3^(-x)*(7 + 2^x + 1), (x, 0, 1))
Gráfica
0.001.000.100.200.300.400.500.600.700.800.90-2020
Trazar el gráfico f(x)
Respuesta [src] 
           9*log(3)                      8*log(2)                      8*log(2)                     10*log(3)          
- ------------------------- - ----------------------------- + ------------------------- + -----------------------------
       2                             2                             2                             2                     
  - log (3) + log(2)*log(3)   - 3*log (3) + 3*log(2)*log(3)   - log (3) + log(2)*log(3)   - 3*log (3) + 3*log(2)*log(3)
8log⁡(2)−log⁡(3)2+log⁡(2)log⁡(3)+10log⁡(3)−3log⁡(3)2+3log⁡(2)log⁡(3)−8log⁡(2)−3log⁡(3)2+3log⁡(2)log⁡(3)−9log⁡(3)−log⁡(3)2+log⁡(2)log⁡(3)\frac{8 \log{\left(2 \right)}}{- \log{\left(3 \right)}^{2} + \log{\left(2 \right)} \log{\left(3 \right)}} + \frac{10 \log{\left(3 \right)}}{- 3 \log{\left(3 \right)}^{2} + 3 \log{\left(2 \right)} \log{\left(3 \right)}} - \frac{8 \log{\left(2 \right)}}{- 3 \log{\left(3 \right)}^{2} + 3 \log{\left(2 \right)} \log{\left(3 \right)}} - \frac{9 \log{\left(3 \right)}}{- \log{\left(3 \right)}^{2} + \log{\left(2 \right)} \log{\left(3 \right)}} 
=
= 
           9*log(3)                      8*log(2)                      8*log(2)                     10*log(3)          
- ------------------------- - ----------------------------- + ------------------------- + -----------------------------
       2                             2                             2                             2                     
  - log (3) + log(2)*log(3)   - 3*log (3) + 3*log(2)*log(3)   - log (3) + log(2)*log(3)   - 3*log (3) + 3*log(2)*log(3)
8log⁡(2)−log⁡(3)2+log⁡(2)log⁡(3)+10log⁡(3)−3log⁡(3)2+3log⁡(2)log⁡(3)−8log⁡(2)−3log⁡(3)2+3log⁡(2)log⁡(3)−9log⁡(3)−log⁡(3)2+log⁡(2)log⁡(3)\frac{8 \log{\left(2 \right)}}{- \log{\left(3 \right)}^{2} + \log{\left(2 \right)} \log{\left(3 \right)}} + \frac{10 \log{\left(3 \right)}}{- 3 \log{\left(3 \right)}^{2} + 3 \log{\left(2 \right)} \log{\left(3 \right)}} - \frac{8 \log{\left(2 \right)}}{- 3 \log{\left(3 \right)}^{2} + 3 \log{\left(2 \right)} \log{\left(3 \right)}} - \frac{9 \log{\left(3 \right)}}{- \log{\left(3 \right)}^{2} + \log{\left(2 \right)} \log{\left(3 \right)}} 
-9*log(3)/(-log(3)^2 + log(2)*log(3)) - 8*log(2)/(-3*log(3)^2 + 3*log(2)*log(3)) + 8*log(2)/(-log(3)^2 + log(2)*log(3)) + 10*log(3)/(-3*log(3)^2 + 3*log(2)*log(3))
Respuesta numérica [src] 
5.67671036280194
5.67671036280194

    Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.

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